Papers by Pedram Hassanzadeh
Optimal Transport from Wall to Wall by Pedram Hassanzadeh
An efficient computational method for thermal radiation in participating media
... Ali Ashrafizadeh for their en-couragement and guidance. Financial supports from CANMET, NSERC... more ... Ali Ashrafizadeh for their en-couragement and guidance. Financial supports from CANMET, NSERC, and the University of Waterloo are gratefully acknowledged. Furthermore, my thanks go to my friends and colleagues Arash Tajik, Sara Toutiaie, Mohsen Shahini, Arman Hajati ...
Baroclinic Vortices in Rotating Stratified Shearing Flows: Cyclones, Anticyclones, and Zombie Vor... more Baroclinic Vortices in Rotating Stratified Shearing Flows: Cyclones, Anticyclones, and Zombie Vortices by Pedram Hassanzadeh
Self-Similar, Self-Replicating, Critical Layers and Vortices in Rotating, Horizontally Shearing, Vertically-Stratified Flows
3D Vortices in Stratified, Rotating Flows-Secondary Circulations and Changes in Aspect Radio Due to Dissipation
ABSTRACT The aspect ratio of a 3D vortex in a rotating, stratified flow is defined as the ratio o... more ABSTRACT The aspect ratio of a 3D vortex in a rotating, stratified flow is defined as the ratio of its vertical half-thickness H to its horizontal scale L. We recently showed that due to hydrostatic and geo/cyclostrophic balance, an anticyclone has an equilibrium scaling law of H/L = Ro (1-Ro) f/(N-Nin), where Ro is the Rossby number of the vortex, f is the Coriolis parameter, and N and Nin are the Brunt-V"ais"al"a frequencies of the local ambient fluid and of the vortex interior, respectively. Introduction of a viscous or thermal dissipation (the latter being much more rapid and therefore much more relevant in atmospheric, astrophysical, and planetary vortices) forces a vortex that was initially in equilibrium to decay through a series of quasi-stationary states. Both viscous and thermal dissipation rapidly induce secondary circulations within the vortex, but the circulations created by the two types of dissipation differ qualitatively from each other. Moreover, thermal dissipation rapidly changes the values of Ro and Nin, so although the equilibrium scaling law above is still satisfied, the aspect ratio of the vortex changes rapidly. We show how the resulting aspect ratio of the vortex, and the magnitude and geometry of the secondary circulation are both strong functions of the vertical dependence of N.
We derive a relationship for the vortex aspect ratio α (vertical half-thickness over horizontal l... more We derive a relationship for the vortex aspect ratio α (vertical half-thickness over horizontal length scale) for steady and slowly evolving vortices in rotating stratified fluids, as a function of the Brunt-Väisälä frequencies within the vortex N c and in the background fluid outside the vortexN, the Coriolis parameter f and the Rossby number Ro of the vortex: α 2 = Ro(1 + Ro)f 2 /(N 2 c −N 2 ). This relation is valid for cyclones and anticyclones in either the cyclostrophic or geostrophic regimes; it works with vortices in Boussinesq fluids or ideal gases, and the background density gradient need not be uniform. Our relation for α has many consequences for equilibrium vortices in rotating stratified flows. For example, cyclones must have N 2 c >N 2 ; weak anticyclones (with |Ro| < 1) must have N 2 c <N 2 ; and strong anticyclones must have N 2 c >N 2 . We verify our relation for α with numerical simulations of the threedimensional Boussinesq equations for a wide variety of vortices, including: vortices that are initially in (dissipationless) equilibrium and then evolve due to an imposed weak viscous dissipation or density radiation; anticyclones created by the geostrophic adjustment of a patch of locally mixed density; cyclones created by fluid suction from a small localized region; vortices created from the remnants of the violent breakups of columnar vortices; and weakly non-axisymmetric vortices. The values of the aspect ratios of our numerically computed vortices validate our relationship for α, and generally they differ significantly from the values obtained from the much-cited conjecture that α = f /N in quasi-geostrophic vortices.
Secondary Flows Within 3D Vortices
Control volume analyses, analytic scaling arguments, and numerical modeling can all be used to sh... more Control volume analyses, analytic scaling arguments, and numerical modeling can all be used to show that in a dissipationless flow that there are classes of 3D vortices in which the fluid velocity is purely 2D. That is, in cylindrical coordinates the vortex occupies a finite region in z so that the vortex has a definite top and bottom, but the
Blocking variability: Arctic Amplification versus Arctic Oscillation
Geophysical Research Letters, 2015
Responses of midlatitude blocks and wave amplitude to changes in the meridional temperature gradient in an idealized dry GCM
Geophysical Research Letters, 2014
Zombie Vortex Instability. I. A Purely Hydrodynamic Instability to Resurrect the Dead Zones of Protoplanetary Disks
The Astrophysical Journal, 2015
Journal of Fluid Mechanics, 2014
The calculus of variations is employed to find steady divergence-free velocity fields that maximi... more The calculus of variations is employed to find steady divergence-free velocity fields that maximize transport of a tracer between two parallel walls held at fixed concentration for one of two constraints on flow strength: a fixed value of the kinetic energy (mean square velocity) or a fixed value of the enstrophy (mean square vorticity). The optimizing flows consist of an array of (convection) cells of a particular aspect ratio Γ . We solve the nonlinear Euler-Lagrange equations analytically for weak flows and numericallyand via matched asymptotic analysis in the fixed energy case-for strong flows. We report the results in terms of the Nusselt number Nu, a dimensionless measure of the tracer transport, as a function of the Péclet number Pe, a dimensionless measure of the strength of the flow. For both constraints the maximum transport Nu MAX (Pe) is realized in cells of decreasing aspect ratio Γ opt (Pe) as Pe increases. For the fixed energy problem, Nu MAX ∼ Pe and Γ opt ∼ Pe −1/2 , while for the fixed enstrophy scenario, Nu MAX ∼ Pe 10/17 and Γ opt ∼ Pe −0.36 . We interpret our results in the context of buoyancy-driven Rayleigh-Bénard convection problems that satisfy the flow intensity constraints, enabling us to investigate how the transport scalings compare with upper bounds on Nu expressed as a function of the Rayleigh number Ra. For steady convection in porous media, corresponding to the fixed energy problem, we find Nu MAX ∼ Ra and Γ opt ∼ Ra −1/2 , while for steady convection in a pure fluid layer between stressfree isothermal walls, corresponding to fixed enstrophy transport, Nu MAX ∼ Ra 5/12 and Γ opt ∼ Ra −1/4 . † The high Reynolds number scaling of a dissipation rate bound is known to be sharp, realized by an exact solution of the Navier-Stokes equations, in at least one case .
The Meridional Secondary Circulation of 3D Vortices in Rotating, Stratified, Shear and its Role in Astrophysical Flows: from a Newly Pale Great Red Spot to Planet Formation
A Universal Diagnostic Equation for the Aspect Ratio of Oceanic Eddies and its Applications: Theory, Simulation, Experiment and Observation
Baroclinic Vortices in Rotating Stratified Shearing Flows: Cyclones, Anticyclones, and Zombie Vor... more Baroclinic Vortices in Rotating Stratified Shearing Flows: Cyclones, Anticyclones, and Zombie Vortices by Pedram Hassanzadeh
On the Effects of Viscosity and Nonlinearity on Baroclinic Critical Layers
Noise and Turbulence Generate 3D Zombie Vortices in Stably Stratified Rotating Shear Flows
3D Zombie Vortices in Rotating Stratified Shear
There is considerable interest in hydrodynamic instabilities in dead zones of protoplanetary disk... more There is considerable interest in hydrodynamic instabilities in dead zones of protoplanetary disks as a mechanism for driving angular momentum transport and as a source of particle-trapping vortices to mix chondrules and incubate planetesimal formation. We present simulations with a pseudo-spectral anelastic code and with the compressible code Athena, showing that stably stratified flows in a shearing, rotating box are violently unstable and produce space-filling, sustained turbulence dominated by large vortices with Rossby numbers of order ∼0.2 − 0.3. This Zombie Vortex Instability (ZVI) is observed in both codes and is triggered by Kolmogorov turbulence with Mach numbers less than ∼0.01. It is a common view that if a given constant density flow is stable, then stable vertical stratification should make the flow even more stable.
Zombie Vortices: Angular Momentum Transport and Planetesimal Formation
On the Surprising Longevity of Jupiter's Centuries-Old Great Red Spot
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Papers by Pedram Hassanzadeh